A finite difference scheme for the equilibrium equations of elastic bodies

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques

The volume in focus: hardwareassisted focus and context effects for volume visualization

In many volume visualization applications there is some region of specific interest where we wish to see fine detail - yet we do not want to lose an impression of the overall picture. In this research we apply the notion of focus and context to texture-based volume rendering. A framework has been developed that enables users to achieve fast volumetric distortion and other effects of practical use. The framework has been implemented through direct programming of the graphics processor and integrated into a volume rendering system. Our driving application is the effective visualization of aneurysms, an important issue in neurosurgery. We have developed and evaluated an easy-to-use system that allows a neurosurgicalteam to explore the nature of cerebral aneurysms, visualizing the aneurysm itself in fine detail while still retaining a view of the surrounding vasculature

A compact finite difference scheme for div(Rho grad u) - q2u = 0

A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation

Knowledge Discovery Using Topological Analysis for Building Sensor Data

Distributed sensor networks are at the heart of smart buildings, providing greater detail and valuable insights into their energy consumption patterns. The problem is particularly complex for older buildings retrofitted with Building Energy Management Systems (BEMS) where extracting useful knowledge from large sensor data streams without full understanding of the underlying system variables is challenging. This paper presents an application of Q-Analysis, a computationally simple topological approach for summarizing large sensor data sets and revealing useful relationships between different variables. Q-Analysis can be used to extract novel structural features called Q-vectors. The Q-vector magnitude visualizations are shown to be very effective in providing insights on macro behaviors, i.e., building floor behaviors in the present case, which are not evident from the use of unsupervised learning algorithms applied on individual terminal units. It has been shown that the building floors exhibited distinct behaviors that are dependent on the set-point distribution, but independent of the time and season of the year

Supersymmetry with Grand Unification

Supersymmetry (SUSY) has many well known attractions, especially in the context of Grand Unified Theories (GUTs). SUSY stabilizes scalar mass corrections (the hierarchy problem), greatly reduces the number of free parameters, facilitates gauge coupling unification, and provides a plausible candidate for cosmological dark matter. In this conference report we survey some recent examples of progress in SUSY-GUT applications.Comment: Talk V. Barger at the Workshop on Physics at Current Accelerators and the Supercollider, Argonne, June 1993, 15 pages + 12 PS figures included (uuencoded), (correct author list in header) MAD/PH/78

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented

ARCS, The Arcminute Radio Cluster-lens Search - I. Selection Criteria and Initial Results

We present the results of an unbiased radio search for gravitational lensing events with image separations between 15 and 60 arcsec, which would be associated with clusters of galaxies with masses >10^{13-14}M_{\sun}. A parent population of 1023 extended radio sources stronger than 35 mJy with stellar optical identifications was selected using the FIRST radio catalogue at 1.4 GHz and the APM optical catalogue. The FIRST catalogue was then searched for companions to the parent sources stronger than 7 mJy and with separation in the range 15 to 60 arcsec. Higher resolution observations of the resulting 38 lens candidates were made with the VLA at 1.4 GHz and 5 GHz, and with MERLIN at 5 GHz in order to test the lens hypothesis in each case. None of our targets was found to be a gravitational lens system. These results provide the best current constraint on the lensing rate for this angular scale, but improved calculations of lensing rates from realistic simulations of the clustering of matter on the relevant scales are required before cosmologically significant constraints can be derived from this null result. We now have an efficient, tested observational strategy with which it will be possible to make an order-of-magnitude larger unbiased search in the near future.Comment: Accepted for publication in MNRAS. 12 pages, 29 included PostScript figure

Coplanar Circumbinary Debris Disks

We present resolved Herschel images of circumbinary debris disks in the alpha CrB (HD139006) and beta Tri (HD13161) systems. We find that both disks are consistent with being aligned with the binary orbital planes. Though secular perturbations from the binary can align the disk, in both cases the alignment time at the distances at which the disk is resolved is greater than the stellar age, so we conclude that the coplanarity was primordial. Neither disk can be modelled as a narrow ring, requiring extended radial distributions. To satisfy both the Herschel and mid-IR images of the alpha CrB disk, we construct a model that extends from 1-300AU, whose radial profile is broadly consistent with a picture where planetesimal collisions are excited by secular perturbations from the binary. However, this model is also consistent with stirring by other mechanisms, such as the formation of Pluto-sized objects. The beta Tri disk model extends from 50-400AU. A model with depleted (rather than empty) inner regions also reproduces the observations and is consistent with binary and other stirring mechanisms. As part of the modelling process, we find that the Herschel PACS beam varies by as much as 10% at 70um and a few % at 100um. The 70um variation can therefore hinder image interpretation, particularly for poorly resolved objects. The number of systems in which circumbinary debris disk orientations have been compared with the binary plane is now four. More systems are needed, but a picture in which disks around very close binaries (alpha CrB, beta Tri, and HD 98800, with periods of a few weeks to a year) are aligned, and disks around wider binaries (99 Her, with a 50 yr period) are misaligned, may be emerging. This picture is qualitatively consistent with the expectation that the protoplanetary disks from which the debris emerged are more likely to be aligned if their binaries have shorter periods.Comment: accepted to MNRA